When Danladi Verheijen has to attend an important meeting, he doesn't know whether getting there will take 10 minutes or three hours. "You're going to upset someone," he says. "You're going to arrive very early or very late. It leads to massive loss of productivity."

But Verheijen believes he can do something to break the deadlock. The 34-year-old venture capitalist is leading a group of investors in Lagos's first city railway. He believes the multibillion-dollar project could transform daily life for millions of people in this uniquely challenging metropolis, and potentially expand west from Nigeria to Ghana.

"I think it will dramatically change the face of Lagos," he said. "One of the lines is in an area people come to in the middle of Lagos island to work. To get to work at 8am, they probably have to leave their house right now about 5.30am or 5.45am. When our trains start working, they can probably leave their home at 7.25am. It's a difference of two hours. If you're saving between two and four hours a day, it's a dramatic effect.

"It's cheaper than the alternative, it's faster, it's safer, it's more reliable, it's more environmentally friendly. So it's very exciting."

Many railways laid during Africa's colonial era have decayed due to neglect, leaving Cecil John Rhodes's Cape-to-Cairo fantasy more remote than ever. In large parts of Nigeria, overgrown tracks and abandoned stations testify to the triumph of cars and planes.

But Lagos is badly in need of mass public transport beyond its recently introduced bus rapid transit system. Nigeria's commercial capital, built on a swamp and a series of islands, will overtake Cairo as Africa's biggest city in the next five years with a population of 12.4 million, according to the UN.

It is hoped that a rail renaissance can be part of the solution. Last year, South Africa launched the R24bn (£2.17bn) Gautrain, linking Johannesburg to its international airport at speeds of up to 100mph, with further expansion to include the administrative capital, Pretoria, a notoriously busy route for motorists.

Lagos's EkoRail – Eko means Lagos in the Yoruba language – is the biggest public-private partnership in Lagos state and will eventually comprise seven railway lines, each costing more than $1bn (£630m). Two lines are already well advanced. The red will run north to south from Lagos island to Agbado through 13 stations. The blue will run 17 miles from the island to Okokomaiko in the middle of an expanded motorway.

It is hoped the lines will carry 1.4 million passengers per day. They will be powered by electricity rather than diesel but, with the national grid notoriously unreliable, EkoRail is building its own 30-40 MW power station, with excess power benefiting the motorway and local communities. The trains could begin test runs late next year.

Reflecting a growing trend in Africa, the project's infrastructure is being built by a Chinese contractor. Verheijen said: "They're much more competitive and aggressive about doing business. They're working Saturdays, they're working Sundays, they're working at nights. They come here and have big housing estates for their staff and just seem to work like armies. It's very focused and things go up very quickly."

Asked who was benefiting from the construction jobs, he said: "A lot of Chinese, some Nigerians as well. I'm not averse to that.

"We need infrastructure. We need toll roads, we need airports, we need rail, we need water transportation systems, we need power. That just allows entrepreneurs to take off from there."

Verheijen said the first goal was to silence the sceptics and show that rail transport was a viable option. But then, encouraged by wider signs of recovery in the national railway sector, he has ambitions to go further in Nigeria and beyond.

"The blue line goes to Badagry [west of Lagos]. It just makes sense to take that on to Togo and to Ghana. It will create trade and move people and also goods across west Africa. It probably sounds ludicrous, it might not even work, but we need to think about expanding in these ways.

"I understand it costs more money to take a container from Lagos to Abuja [the Nigerian capital] than it does to ship one from China to Lagos. Unbelievable. Rail, hopefully, will change a lot of that."

Verheijen hopes that one day Lagosians will find the railway as indispensable as Londoners. "I think as businesses get more competitive, people care a lot more about their time. Ten years ago we didn't have mobile phones and every time you had a message, you literally had to send somebody. We've become a lot more efficient now with the proliferation of mobile phones and can't even imagine ourselves living in that era. I'm sure rail transportation will be the same here.

"Ten years from now, we will not be able to imagine how we were able to slug through traffic every day."

Some veterans of Lagos's go-slow traffic arteries have welcomed the new scheme. Tolu Ogunlesi, a journalist and author, would leave home at 5.45am to reach his office at 8am. "It's not unusual to find Lagosians waking at 4am so they can be sure of getting to the office at eight," he said. "It's a crazy life.

"I'd definitely use the Lagos rail. I think it's pure insanity for anyone to assume that Lagos's traffic problems can be solved without a means of moving large numbers of people between the mainland and the island with minimum delay outside of the existing road system. And what would that be if not a rail system?

"So far the government has tried buses and bus lanes, but clearly something more imaginative, and drastic, is required. Imagine what London would be without the tube – and Lagos has more people than London."